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DOE OSTI2022

A 1D–0D–3D coupled model for simulating blood flow and transport processes in breast tissue

In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are considered, to start from the aortic inlet to the capillaries and tissue of the breast. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic partial differential equations (PDEs) is considered to simulate blood flow in larger arteries with highly elastic vessel walls. Second, we assign 1D linearized hyperbolic PDEs to model the smaller arteries with stiffer vessel walls. The third model type consists of ODE systems (0D models). It is used to model the arterioles and peripheral circulation. Finally, homogenized 3D porous media models are considered to simulate flow and transport in capillaries and tissue within the breast volume. Sink terms are used to account for the influence of the venous and lymphatic systems. Combining the four model types, we obtain two different 1D–0D–3D coupled models for simulating blood flow and transport processes: The first model results in a fully coupled 1D–0D–3D model covering the complete path from the aorta to the breast combining a generic arterial network with a patient specific breast network and geometry. The second model is a reduced one based on the separation of the generic and patient specific parts. The information from a calibrated fully coupled model is used as inflow condition for the patient specific sub-model allowing a significant computational cost reduction. Several numerical experiments are conducted to calibrate the generic model parameters and to demonstrate realistic flow simulations compared to existing data on blood flow in the human breast and vascular system. Moreover, we use two different breast vasculature and tissue data sets to illustrate the robustness of our reduced sub-model approach.

multiscale blood flow models↗

DOE OSTI2020

Biomimetic Rebuilding of Multifunctional Red Blood Cells: Modular Design Using Functional Components

The design and synthesis of artificial materials that mimic the structures, mechanical properties, and ultimately functionalities of biological cells remains a current holy grail of materials science. Here based on a silica cell bio-replication approach, we report the design and construction of synthetic rebuilt red blood cells (RRBCs) that fully mimic the broad properties of native RBCs: size, biconcave shape, deformability, oxygen carrying capacity, long circulation time. Four successive nano-scale processing steps: RBC bioreplication, layer-by-layer polymer deposition, and precision silica etching, followed by RBC ghost membrane vesicles fusion are employed for RRBC construction. A panel of physicochemical analyses including zeta potential measurement, fluorescence microscopy, and antibody-mediated agglutination assay proved the recapitulation of RBC shape, size, and membrane structure. Flow-based deformation studies carried out in a microfluidic blood capillary model confirrned the ability of RRBCs to deform and pass through small slits and reconstitute themselves in a manner comparable to native RBCs. Circulation studies of RRBCs conducted ex-ovo in a chick embryo and in vivo in a mouse model demonstrated the requirement of both deformability and native cell membrane surface to achieve long-term circulation. To confer additional non-native functionalities to RRBCs, we developed modular procedures in which to load functional cargos such as hemoglobin, drugs, magnetic nanoparticles, and ATP biosensors within the RRBC interior to enable various functions, including oxygen delivery, therapeutic drug delivery, magnetic manipulation, and toxin biosensing and detection. Taken together, RRBCs represent a class of long circulating RBC-inspired artificial hybrid materials with a broad range of potential applications.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Numerical algorithms for water waves with background flow over obstacles and topography

Abstract We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface, are compatible with arbitrary parameterizations of the free surface and boundaries, and allow for circulation around each obstacle, which leads to multiple-valued velocity potentials but single-valued stream functions. We prove that the resulting second-kind Fredholm integral equations are invertible, possibly after a physically motivated finite-rank correction. In an angle-arclength setting, we show how to avoid curve reconstruction errors that are incompatible with spatial periodicity. We use the proposed methods to study gravity-capillary waves generated by flow around several elliptical obstacles above a flat or variable bottom boundary. In each case, the free surface eventually self-intersects in a splash singularity or collides with a boundary. We also show how to evaluate the velocity and pressure with spectral accuracy throughout the fluid, including near the free surface and solid boundaries. To assess the accuracy of the time evolution, we monitor energy conservation and the decay of Fourier modes and compare the numerical results of the two methods to each other. We implement several solvers for the discretized linear systems and compare their performance. The fastest approach employs a graphics processing unit (GPU) to construct the matrices and carry out iterations of the generalized minimal residual method (GMRES).

Ambrose, David M.↗

DOE OSTI2022

Ultrafast two-photon fluorescence imaging of cerebral blood circulation in the mouse brain in vivo

Characterizing blood flow dynamics in vivo is critical to understanding the function of the vascular network under physiological and pathological conditions. Existing methods for hemodynamic imaging have insufficient spatial and temporal resolution to monitor blood flow at the cellular level in large blood vessels. By using an ultrafast line-scanning module based on free-space angular chirped enhanced delay, we achieved two-photon fluorescence imaging of cortical blood flow at 1,000 two-dimensional (2D) frames and 1,000,000 one-dimensional line scans per second in the awake mouse. This orders-of-magnitude increase in temporal resolution allowed us to measure cerebral blood flow at up to 49 mm/s and observe pulsatile blood flow at harmonics of heart rate. Directly visualizing red blood cell (RBC) flow through vessels down to >800 µm in depth, we characterized cortical layer–dependent flow velocity distributions of capillaries, obtained radial velocity profiles and kilohertz 2D velocity mapping of multifile blood flow, and performed RBC flux measurements from penetrating blood vessels.

59 BASIC BIOLOGICAL SCIENCES↗